5a(a+3)=4(2a+3)

Solution for 5a(a+3)=4(2a+3) equation:

5a(a+3)=4(2a+3)

We move all terms to the left:

5a(a+3)-(4(2a+3))=0

We multiply parentheses

5a^2+15a-(4(2a+3))=0


We calculate terms in parentheses: -(4(2a+3)), so:

4(2a+3)

We multiply parentheses

8a+12

Back to the equation:

-(8a+12)


We get rid of parentheses

5a^2+15a-8a-12=0

We add all the numbers together, and all the variables

5a^2+7a-12=0

a = 5; b = 7; c = -12;
Δ = b2-4ac
Δ = 72-4·5·(-12)
Δ = 289
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{289}=17$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(7)-17}{2*5}=\frac{-24}{10}
=-2+2/5
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(7)+17}{2*5}=\frac{10}{10}
=1
$